The 40-year-old tested positive only days after she returned from her lavish but controversial $1 million birthday bash on a private island in Tahiti in October.
However, Kardashian clarified that "Nobody caught Covid from the trip".
"Saint was the first to have it in our family and he caught it from school from another student who tested positive first. I then developed symptoms and got it a few days after he coughed on me while caring for him," she explained.
On Keeping up with the Kardashians, Kim shared that she did not pass her first-year law school exam and then Saint tested positive weeks before she was to retake it.
The SKIMS founder explained that her children were getting tested once a week in order to go to their school "pod".
"Saint has COVID, and I'm just really worried about him. He's crying and coughing on me, and I'm trying to not freak anyone out, but now I have to figure out what we're gonna do — especially with the three other kids," she explained.
Kardashian then got in touch with her family doctor because North was feeling unwell. "North is saying she's feeling sick, and I slept in bed with her last night. She tested negative, but I'm gonna test her again with me on Saturday," Kim told the doctor.
With the "baby bar exam" looming, Kardashian decided to be there for her children. "Taking care of my kids comes first," she explained.
Kardashian and the rest of her children then tested positive for COVID-19, which shut down production of KUWTK for 14 days while the family and crew had to quarantine.
However, Kardashian kept the show going by recording herself on her phone and webcams. While she tried to study, her symptoms such as nausea, coughs and aches and pains made things difficult.
"We're supposed to be doing 12-hour study sessions every day leading up to the test, and I've just been feeling so sick and so just awful with COVID that I can hardly even get out of bed and study," Kim explained.
Kardashian decided to take the test, rather than wait another six months before she could sit it again. "If I feel like I do now, it's gonna be really hard to sit up and take a test for seven hours. And I'm on heavy medication right now," she explained.
"It's frustrating, because I should be in full study mode and tune everything out. But it's so hard, and I just want to give up," she lamented.
Although she wasn't feeling great when the test came around, Kardashian still sat it. "I am so tired. I did it, though. I pulled through. Even if I don't pass, it's OK," she explained.
"That was the hardest thing I've ever, ever had to do.... I definitely feel like I knew more this time on the test than last time on the test. I feel really confident about that," Kardashian shared later. "If I do pass, it's a miracle, because I had COVID!"
After the hologram said he was proud of his daughter for pursuing law, she decided to retake the exam.